Math / Numbers & Operations

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If there are 36 apples and 60 bananas for a fruit basket, fill out all of the possible ratios of app to bananas that could be made.
There are 36 apples for every 60 bananas ( $36: 60$ ratio) There are $\square$ apples for every $\square$ bananas $\square$ Type in an equivalent ratio of apples and bananas.

Studdy Solution

STEP 1

1. We have a total of 36 apples and 60 bananas.
2. We need to find all possible equivalent ratios of apples to bananas.
3. Ratios can be simplified by dividing both terms by their greatest common divisor (GCD).

STEP 2

1. Simplify the given ratio.
2. Determine all equivalent ratios.

STEP 3

Identify the initial ratio of apples to bananas, which is $36:60$ .

STEP 4

Find the greatest common divisor (GCD) of 36 and 60.
- The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36. - The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. - The common factors are: 1, 2, 3, 4, 6, 12. - The greatest common factor is 12.

STEP 5

Simplify the ratio $36:60$ by dividing both numbers by their GCD, which is 12.
$\frac{36}{12} : \frac{60}{12} = 3:5$

STEP 6

List all equivalent ratios by multiplying the simplified ratio $3:5$ by integer values.
- Multiply by 1: $3 \times 1 : 5 \times 1 = 3:5$ - Multiply by 2: $3 \times 2 : 5 \times 2 = 6:10$ - Multiply by 3: $3 \times 3 : 5 \times 3 = 9:15$ - Multiply by 4: $3 \times 4 : 5 \times 4 = 12:20$ - Multiply by 5: $3 \times 5 : 5 \times 5 = 15:25$ - Multiply by 6: $3 \times 6 : 5 \times 6 = 18:30$ - Multiply by 7: $3 \times 7 : 5 \times 7 = 21:35$ - Multiply by 8: $3 \times 8 : 5 \times 8 = 24:40$ - Multiply by 9: $3 \times 9 : 5 \times 9 = 27:45$ - Multiply by 10: $3 \times 10 : 5 \times 10 = 30:50$ - Multiply by 11: $3 \times 11 : 5 \times 11 = 33:55$ - Multiply by 12: $3 \times 12 : 5 \times 12 = 36:60$
The possible equivalent ratios of apples to bananas are: $3:5, 6:10, 9:15, 12:20, 15:25, 18:30, 21:35, 24:40, 27:45, 30:50, 33:55, 36:60$

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Studdy Solution

STEP 1

1. We have a total of 36 apples and 60 bananas.
2. We need to find all possible equivalent ratios of apples to bananas.
3. Ratios can be simplified by dividing both terms by their greatest common divisor (GCD).

STEP 2

1. Simplify the given ratio.
2. Determine all equivalent ratios.

STEP 3

Identify the initial ratio of apples to bananas, which is $36:60$ .

STEP 4

Find the greatest common divisor (GCD) of 36 and 60.
- The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36. - The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. - The common factors are: 1, 2, 3, 4, 6, 12. - The greatest common factor is 12.

STEP 5

Simplify the ratio $36:60$ by dividing both numbers by their GCD, which is 12.
$\frac{36}{12} : \frac{60}{12} = 3:5$

STEP 6

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Studdy Solution

STEP 1

1. We have a total of 36 apples and 60 bananas.2. We need to find all possible equivalent ratios of apples to bananas.3. Ratios can be simplified by dividing both terms by their greatest common divisor (GCD).

STEP 2

1. Simplify the given ratio.2. Determine all equivalent ratios.

STEP 3

Identify the initial ratio of apples to bananas, which is 36:60 36:60 36:60.

STEP 4

Find the greatest common divisor (GCD) of 36 and 60.- The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36. - The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. - The common factors are: 1, 2, 3, 4, 6, 12. - The greatest common factor is 12.

STEP 5

Simplify the ratio 36:60 36:60 36:60 by dividing both numbers by their GCD, which is 12.3612:6012=3:5\frac{36}{12} : \frac{60}{12} = 3:51236​:1260​=3:5

STEP 6

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. We have a total of 36 apples and 60 bananas.
2. We need to find all possible equivalent ratios of apples to bananas.
3. Ratios can be simplified by dividing both terms by their greatest common divisor (GCD).

1. Simplify the given ratio.
2. Determine all equivalent ratios.

Identify the initial ratio of apples to bananas, which is $36:60$ .

Find the greatest common divisor (GCD) of 36 and 60.
- The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36. - The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. - The common factors are: 1, 2, 3, 4, 6, 12. - The greatest common factor is 12.

Simplify the ratio $36:60$ by dividing both numbers by their GCD, which is 12.
$\frac{36}{12} : \frac{60}{12} = 3:5$